Question

which of the following equation has root -2 and 7​

Answer 1

Answer:

x^2+5x-14 is the equation

Step-by-step explanation:

alpha =-2

beta =7

equation is x^2+(alpha+beta)x+(alpha,*beta)

x^2+5x-14

Answer 2

The required equation is x² - 5x - 14 = 0

Given :

The roots of a equation are - 2 & 7

To find :

The equation is

a) x² – 5x + 14 = 0

b) x² + 5x -14 = 0

c) x² – 5x - 14 = 0

d) x² + 5x + 14 = 0

Concept :

The quadratic equation whose zeroes are given can be written as

$\sf {x}^{2} - (Sum \:of \:the \: roots )x + (Product \:of \:the \: roots ) = 0$

Solution :

Step 1 of 3 :

Write down the roots of the equation

Here it is given that roots of the equation are - 2 & 7

Step 2 of 3 :

Find sum of roots and product of the roots

Sum of the roots = - 2 + 7 = 5

Product of the roots = - 2 × 7 = - 14

Step 3 of 3 :

Find the equation

So the required Quadratic equation is given by

$\sf {x}^{2} - (Sum \:of \:the \: roots )x + (Product \:of \:the \: roots ) = 0$

$\displaystyle \sf{ \implies {x}^{2} - 5x - 14 = 0}$

Hence the correct option is c) x² – 5x - 14 = 0

Correct question : Which of the following equation has roots -2 and 7 ? a) x² – 5x + 14 = 0 b) x² + 5x -14 = 0 c) x² – 5x - 14 = 0 d) x² + 5x + 14 = 0